Abstract
For decades, the algorithm providing the smallest proven worst-case running time (with respect to the number of terminals) for the Steiner tree problem has been the one by Dreyfus and Wagner. In this paper, a new algorithm is developed, which improves the running time from O(3k n+2k n 2+n 3) to (2+δ)k ·poly(n) for arbitrary but fixed δ > 0. Like its predecessor, this algorithm follows the dynamic programming paradigm. Whereas in effect the Dreyfus–Wagner recursion splits the optimal Steiner tree in two parts of arbitrary sizes, our approach looks for a set of nodes that separate the tree into parts containing only few terminals. It is then possible to solve an instance of the Steiner tree problem more efficiently by combining partial solutions.
Supported by the DFG under grant RO 927/6-1 (TAPI).
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References
Beigel, R.: Finding maximum independent sets in sparse and general graphs. In: SODA10th, pp. 856–857 (1999)
Bern, M., Plassmann, P.: The Steiner problem with edge lengths 1 and 2. IPL 32, 171–176 (1989)
Dreyfus, S.E., Wagner, R.A.: The Steiner problem in graphs. Networks 1, 195–207 (1972)
Fomin, F.V., Grandoni, F., Kratsch, D.: Measure and conquer: Domination – A case study. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, Springer, Heidelberg (2005)
Iwama, K., Tamaki, S.: Improved upper bounds for 3-SAT. In: SODA15th, pp. 328–328 (2004)
Kneis, J., Mölle, D., Richter, S., Rossmanith, P.: Algorithm based on the treewidth of sparse graphs. In: Kratsch, D. (ed.) WG 2005. LNCS, vol. 3787, Springer, Heidelberg (2005)
Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: SODA11th, pp. 770–779 (2000)
Robson, J.M.: Algorithms for maximum independent sets. Journal of Algorithms 7, 425–440 (1986)
Scott, A., Sorkin, G.B.: Faster algorithms for Max-CUT and Max-CSP, with polynomial expected time for sparse instances. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds.) RANDOM 2003 and APPROX 2003. LNCS, vol. 2764, pp. 382–395. Springer, Heidelberg (2003)
Williams, R.: A new algorithm for optimal constraint satisfaction and its implications. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 1227–1237. Springer, Heidelberg (2004)
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Mölle, D., Richter, S., Rossmanith, P. (2006). A Faster Algorithm for the Steiner Tree Problem. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_46
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DOI: https://doi.org/10.1007/11672142_46
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